This isn't really true. The issue is that when you combine data across multiple MRI scanners (sites), you need to account for random effects (e.g. site specific means and variances)...see solutions like COMBAT. Also if they have different equipment versions/manufacturers those scanners can have different SNR profiles. The other issue is that there are many processing with many ways to perform those steps. In general, researchers don't process in multiple ways and choose the way that gives them the result they want or anything nefarious like that, but it does make comparisons difficult since the effects of different preprocessing variations can be significant. To defend against this, many peer reviewers, like myself, request researchers perform the preprocessing multiple ways to assess how robust the results are to those choices. Another way the field has combatted this issue has been software like fMRIprep.

The source in the other comment seems to disagree with your statements. The science simply isn't that good on a fundamental level and then there's tons of biological and engineering limited noise on top of it.